Crystalline Solids CaF2 Unit Cell Crystal Lattice – A 3D array of points where each point has an identical environment. Unit Cell – The repeating unit (a unit cell is to a crystal, like a “brick” is in a house). In a given crystal all unit cells are identical.

Ionic radii and coordination number Cation Anion Large cation & Large anion r(Cation)/r(Anion) ~0.72 Small cation & Large anion r(Cation)/r(Anion) ~0.3 Anions and cations want to stay in contact with each other, but when the cation becomes much smaller than the anion, anion-anion contacts prevent this. The solution is to lower the coordination number

Coordination Geometry Radius Ratio Rules r(cation)/r(anion) Coordination Number Coordination Geometry  0.73 8 Cube  0.41 6 Octahedron  0.22 4 Tetrahedron  0.15 3 Trigonal Planar These are only meant to be used as rough guidelines, but the coordination number does goes down as the radius ratio [r(cation)/r(anion)] decreases.

Ionic Crystal Structures (a) CsCl (b) NaCl (c) Zinc blende Decreasing coordination number Decreasing r(cation)/r(anion)

Cell Edge vs. Radii 4rFe = √3 a 2rRe + 2rO = a 4rAg = √2 a Body centered cubic metal (i.e. Fe) Face centered cubic metal (i.e. Ag) ReO3 structure a diag a diag a 4rFe = √3 a 2rRe + 2rO = a 4rAg = √2 a Atoms touch along the body diagonal of the cubic unit cell Atoms touch along a face diagonal of the cubic unit cell Atoms touch along an edge of the cubic unit cell

Optical Diffraction Experiment Laser Diffraction Slide Diffraction Spots

Diffraction Demo Take home message The diffraction pattern is related but not equal to the grid pattern Diffraction is most effective for monochromatic light whose wavelength is similar to the spacing of “slits” For crystals X-rays have a wavelength comparable to spacings of atoms

Single Crystal X-ray Diffraction

Bragg’s Law A B d The extra path length traveled by wave B (shown in red) is equal to 2d sin q, where d is the spacing between planes. Constructive interference will only occur if this distance is an integer multiple of the wavelength (nl).

X-ray Powder Diffraction q 2q Horizontal Diffraction Circle Divergent X-ray Source Detector Divergence Slit Antiscatter Slit Receiving Slit Horizontal Soller Slits Sample (Vertical Flat Plate)

X-ray Powder Diffraction Pattern